Self-consistent calculation of the flux-flow conductivity in diffusive superconductors

In the framework of Keldysh-Usadel kinetic theory, we study the temperature dependence of flux-flow conductivity (FFC) in diffusive superconductors. By using self-consistent vortex solutions we find the exact values of dimensionless parameters that determine the diffusion-controlled FFC both in the limit of the low temperatures and close to the critical one. Taking into account the electron-phonon scattering, we study the transition between flux-flow regimes controlled by either the diffusion or the inelastic relaxation of nonequilibrium quasiparticles. We demonstrate that the inelastic electron-phonon relaxation leads to the strong suppression of FFC compared to the previous estimates, making it possible to obtain numerical agreement with experimental results.